Finite Group Databasebeta

← #14769464

Subgroups — #14769464

Order 2816.

1494 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082099C211yesmaximal, characteristic
2#13077348C211yesmaximal, characteristic, complemented
3C2×#10622434C211yesmaximal, characteristic, complemented
4C22×#66869C211yesmaximal, characteristic, complemented
5#13071059C211yesmaximal, characteristic, complemented
6#13069533C211yesmaximal, characteristic, complemented
7#13069446C211yesmaximal, characteristic, complemented
8#13069063C211yesmaximal, characteristic, complemented
9#13068919C211yesmaximal, characteristic, complemented
10#13068917C211yesmaximal, characteristic, complemented
11#13068635C211yesmaximal, characteristic, complemented
12#13068559C211yesmaximal, characteristic, complemented
13#13068558C211yesmaximal, characteristic, complemented
14#13068425C211yesmaximal, characteristic, complemented
15C11×#1896C211yesmaximal, characteristic, complemented
16C2×#41×D11C2211yescharacteristic
17C22×#4339C2211yescharacteristic
18C11×#525C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic, complemented
20#10623363C2211yescharacteristic
21C2×C4×C22⋊D11C2211yescharacteristic
22C22×#4318C2211yescharacteristic, complemented
23C2×M16×D11C2211yescharacteristic, complemented
24#10623186—21no—
25#10623185—21no—
26#10623164C411yescharacteristic, complemented
27#10623163C411yescharacteristic, complemented
28#10623162C411yescharacteristic, complemented
29#10623161C411yescharacteristic, complemented
30#10623143C411yescharacteristic, complemented
31#10623140C411yescharacteristic, complemented
32#10623130C411yescharacteristic, complemented
33#10623129C411yescharacteristic, complemented
34#10623122—21no—
35#10623121—21no—
36#10623079—21no—
37#10623078—21no—
38#10623078—21no—
39C4×D4×D11—21no—
40#10623055C2211yescharacteristic
41#10623053C2211yescharacteristic
42C2×#66925C2211yescharacteristic, complemented
43C2×C11×#104C2211yescharacteristic, complemented
44C2×C11×#104C2211yescharacteristic, complemented
45C11×#407C2211yescharacteristic, complemented
46C2×#66901C2211yescharacteristic, complemented
47C2×#66901C2211yescharacteristic, complemented
48#10622826—21no—
49#10622823—21no—
50C4×C22⋊Dic11C2211yescharacteristic, complemented
51C2×#66889C2211yescharacteristic
52C2×#66889C2211yescharacteristic
53C2×#66889C2211yescharacteristic, complemented
54C2×#66889C2211yescharacteristic, complemented
55#10622739C2211yescharacteristic, complemented
56#10622731C2211yescharacteristic, complemented
57M16×Dic11C2211yescharacteristic, complemented
58#10622553—21no—
59C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
60#10622546—21no—
61#10622545C2211yescharacteristic, complemented
62C4×Dic11⋊C4C2211yescharacteristic, complemented
63C2×#66869—24no—
64C2×#66869C2211yescharacteristic
65C2×#66869C2211yescharacteristic
66C2×#66869C2211yescharacteristic, complemented
67C2×#66869C2211yescharacteristic, complemented
68#10622434—24no—
69#10622343—21no—
70#10622342—21no—
71#10622341—21no—
72(C22⋊D11)⋊C8—21no—
73C11×#339C2211yescharacteristic, complemented
74C11×#339C2211yescharacteristic, complemented
75#10622170C2211yescharacteristic, complemented
76#10622170C2211yescharacteristic, complemented
77C2×C11×#41C2311yescharacteristic
78C23×C4×C11—21no—
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11—21no—
81C22×C22⋊D11D411yescharacteristic
82#41×D11—22no—
83#41×D11—22no—
84#41×D11—41no—
85#41×D11—41no—
86C2×#4343C2×C411yescharacteristic, complemented
87C2×Q8×D11C2×C411yescharacteristic, complemented
88C2×#4341—21no—
89C2×#4341C2×C411yescharacteristic, complemented
90C2×D4×D11—21no—
91C2×D4×D11—21no—
92C2×D4×D11C2×C411yescharacteristic, complemented
93C2×#4339—21no—
94C2×#4339—21no—
95C2×#4339—21no—
96C2×#4339—22no—
97C2×#4339—22no—
98C2×#4339—41no—
99C2×#4339—41no—
100C2×#4339C2×C411yescharacteristic
101C2×#4339C2×C411yescharacteristic
102C2×#4339C2311yescharacteristic
103C2×#4339C2311yescharacteristic
104C22×D44C2×C411yescharacteristic
105C22×C4×D11—21no—
106C22×C4×D11—21no—
107C22×C4×D11C2311yescharacteristic
108C22×Dic22C2×C411yescharacteristic
109C2×C11×M16C2311yescharacteristic
110C2×C11×M16C2311yescharacteristic
111C11×#123—21no—
112C11×C22⋊Q8C2×C411yescharacteristic
113C11×C22⋊Q8C2×C411yescharacteristic
114C11×#121C2×C411yescharacteristic
115C11×#121C2×C411yescharacteristic
116C11×#120—21no—
117C4×D4×C11—21no—
118C4×D4×C11—21no—
119C11×#117C2311yescharacteristic
120C2×C42×C11—22no—
121C2×C42×C11—21no—
122C2×C42×C11—41no—
123C2×C42×C11C2311yescharacteristic
124C2×C42×C11C2311yescharacteristic
125C2×C22⋊Dic11—21no—
126C2×C22⋊Dic11D411yescharacteristic
127#67000C2×C411yescharacteristic, complemented
128#66997C2×C411yescharacteristic, complemented
129#66993—21no—
130#66993C2×C411yescharacteristic, complemented
131#66992—21no—
132#66992—21no—
133#66992—21no—
134#66992—21no—
135#66991—21no—
136#66990—21no—
137#66990—21no—
138#66989C2×C411yescharacteristic, complemented
139D4×Dic11—21no—
140C4×C22⋊D11—21no—
141C4×C22⋊D11—21no—
142C4×C22⋊D11C2×C411yescharacteristic
143C4×C22⋊D11C2×C411yescharacteristic
144C4×C22⋊D11C2×C411yescharacteristic
145C4×C22⋊D11C2×C411yescharacteristic
146C4×C22⋊D11D411yescharacteristic
147C4×C22⋊D11D411yescharacteristic
148C4×C22⋊D11D411yescharacteristic
149C4×C22⋊D11D411yescharacteristic
150C2×(C2×D11)⋊C4—21no—
151C2×(C2×D11)⋊C4—21no—
152C2×(C2×D11)⋊C4D411yescharacteristic
153C2×Dic11⋊C4—21no—
154C2×Dic11⋊C4—21no—
155C2×Dic11⋊C4D411yescharacteristic
156C2×C4×Dic11C2311yescharacteristic
157C2×C4×Dic11C2311yescharacteristic
158C2×C4×Dic11C2311yescharacteristic
159C2×#4318—21no—
160C2×#4318—22no—
161C2×#4318—41no—
162C2×#4318C2311yescharacteristic
163C2×#4318C2311yescharacteristic
164C22×C11⋊C8—21no—
165M16×D11—22no—
166M16×D11—41no—
167C2×#4313—21no—
168C2×C8×D11—21no—
169#66950C2×C411yescharacteristic, complemented
170#66950C2×C411yescharacteristic, complemented
171#66949—21no—
172#66949—21no—
173#66948—21no—
174#66948C2×C411yescharacteristic, complemented
175#66948C2×C411yescharacteristic, complemented
176#66947—21no—
177#66947—21no—
178#66946—21no—
179#66946C2×C411yescharacteristic, complemented
180#66946C2×C411yescharacteristic, complemented
181C4⋊C4×D11—21no—
182#66941—21no—
183#66940C2×C411yescharacteristic, complemented
184#66940C2×C411yescharacteristic, complemented
185#66939—21no—
186#66938—21no—
187#66938—21no—
188#66937—21no—
189#66937—21no—
190#66937—21no—
191#66937—21no—
192#66936—21no—
193#66936—21no—
194#66935—21no—
195#66935—21no—
196#66935—21no—
197(C22⋊D11)⋊C4—21no—
198(C22⋊D11)⋊C4—21no—
199(C22⋊D11)⋊C4—21no—
200(C22⋊D11)⋊C4—21no—
201C22⋊C4×D11—21no—
202C22⋊C4×D11—21no—
203#66931—21no—
204#66931—21no—
205C4×D44—21no—
206C4×D44—21no—
207#66925—22no—
208#66925—21no—
209#66925—41no—
210C42×D11—21no—
211C11×#104—22no—
212C11×#104—41no—
213C11×C22⋊C8—21no—
214C11×C22⋊C8—21no—
215#66901—22no—
216#66901—41no—
217C11⋊#95—21no—
218C11⋊#95—21no—
219C11⋊#95—21no—
220C11⋊#95—21no—
221C11⋊#95—21no—
222#66889—22no—
223#66889—22no—
224#66889—41no—
225#66889—41no—
226(C2×D11)⋊C8—21no—
227(C2×D11)⋊C8—21no—
228#66879—21no—
229Dic11⋊C8—21no—
230Dic11⋊C8—21no—
231C8×Dic11—21no—
232#66869—22no—
233#66869—22no—
234#66869—22no—
235#66869D414yescomplemented
236#22434—111nomaximal, Sylow
237C24×C11C2×D411yescharacteristic
238C23×D11—21no—
239C23×D11—21no—
240C23×D11C2×D411yescharacteristic
241C11×#41—21no—
242C11×#41—21no—
243C11×#41—21no—
244C11×#41—21no—
245C2×Q8×C11C22×C411yescharacteristic
246C2×D4×C11—21no—
247C2×D4×C11—21no—
248C2×D4×C11—21no—
249C2×D4×C11C22×C411yescharacteristic
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—21no—
254C22×C4×C11—21no—
255C22×C4×C11—21no—
256C22×C4×C11—21no—
257C22×C4×C11—42no—
258C22×C4×C11—42no—
259C22×C4×C11—42no—
260C22×C4×C11C22×C411yescharacteristic
261C22×C4×C11C22×C411yescharacteristic
262C22×C4×C11C2×D411yescharacteristic
263C22×C4×C11C2×D411yescharacteristic
264C22×C4×C11C2×D411yescharacteristic
265C22×C4×C11C2411yescharacteristic
266C2×C22⋊D11—21no—
267C2×C22⋊D11—21no—
268C2×C22⋊D11—21no—
269C2×C22⋊D11—21no—
270C2×C22⋊D11—21no—
271C2×C22⋊D11—21no—
272C2×C22⋊D11—21no—
273C2×C22⋊D11—21no—
274C2×C22⋊D11—42no—
275C2×C22⋊D11—42no—
276C2×C22⋊D11—42no—
277C2×C22⋊D11C22⋊C411yescharacteristic
278C2×C22⋊D11C22⋊C411yescharacteristic
279C2×C22⋊D11C22⋊C411yescharacteristic
280C2×C22⋊D11C22⋊C411yescharacteristic
281C22×Dic11—21no—
282C22×Dic11—21no—
283C22×Dic11—21no—
284C22×Dic11—21no—
285C22×Dic11C2×D411yescharacteristic
286C22×Dic11C2×D411yescharacteristic
287C22×Dic11C2×D411yescharacteristic
288#4343—22no—
289#4343—41no—
290Q8×D11—22no—
291Q8×D11—41no—
292#4341—22no—
293#4341—41no—
294#4341—42no—
295#4341—42no—
296D4×D11—22no—
297D4×D11—41no—
298D4×D11—42no—
299D4×D11—42no—
300D4×D11—44no—
301#4339—22no—
302#4339—22no—
303#4339—21no—
304#4339—21no—
305#4339—21no—
306#4339—21no—
307#4339—21no—
308#4339—21no—
309#4339—41no—
310#4339—41no—
311#4339—42no—
312#4339—42no—
313#4339—42no—
314#4339—42no—
315#4339—42no—
316#4339—42no—
317#4339C2×D412yes—
318#4339#4112yes—
319C2×D44—21no—
320C2×D44—21no—
321C2×D44—21no—
322C2×D44—22no—
323C2×D44—21no—
324C2×D44—41no—
325C2×D44C22×C411yescharacteristic
326C2×D44C22×C411yescharacteristic
327C2×C4×D11—21no—
328C2×C4×D11—21no—
329C2×C4×D11—21no—
330C2×C4×D11—21no—
331C2×C4×D11—21no—
332C2×C4×D11—21no—
333C2×C4×D11—21no—
334C2×C4×D11—21no—
335C2×C4×D11—21no—
336C2×C4×D11—21no—
337C2×C4×D11—21no—
338C2×C4×D11—21no—
339C2×C4×D11—42no—
340C2×C4×D11—42no—
341C2×C4×D11—42no—
342C2×C4×D11—42no—
343C2×C4×D11C22×C411yescharacteristic
344C2×C4×D11C22×C411yescharacteristic
345C2×C4×D11C2×D411yescharacteristic
346C2×C4×D11C2×D411yescharacteristic
347C2×Dic22—22no—
348C2×Dic22—21no—
349C2×Dic22—21no—
350C2×Dic22—41no—
351C2×Dic22C22×C411yescharacteristic
352C2×Dic22C22×C411yescharacteristic
353C11×M16—21no—
354C11×M16—21no—
355C11×M16—21no—
356C11×M16—21no—
357C2×C8×C11—21no—
358C2×C8×C11—21no—
359C11×C4⋊C4—21no—
360C11×C4⋊C4—21no—
361C11×C4⋊C4C22×C411yescharacteristic
362C11×C4⋊C4C22×C411yescharacteristic
363C11×C22⋊C4—21no—
364C11×C22⋊C4—21no—
365C11×C22⋊C4—21no—
366C11×C22⋊C4—21no—
367C11×C22⋊C4—21no—
368C42×C11—21no—
369C42×C11—21no—
370C42×C11—21no—
371C42×C11—21no—
372C42×C11—42no—
373C42×C11C2×D412yescomplemented
374C22⋊Dic11—21no—
375C22⋊Dic11—21no—
376C22⋊Dic11—42no—
377C22⋊Dic11C22⋊C411yescharacteristic
378C22⋊Dic11C22⋊C411yescharacteristic
379C22⋊Dic11C22⋊C411yescharacteristic
380C22⋊Dic11C22⋊C411yescharacteristic
381(C2×D11)⋊C4—21no—
382(C2×D11)⋊C4—21no—
383(C2×D11)⋊C4—21no—
384(C2×D11)⋊C4—21no—
385(C2×D11)⋊C4—21no—
386(C2×D11)⋊C4—21no—
387(C2×D11)⋊C4—21no—
388(C2×D11)⋊C4—21no—
389(C2×D11)⋊C4—42no—
390(C2×D11)⋊C4—42no—
391(C2×D11)⋊C4C22⋊C411yescharacteristic
392(C2×D11)⋊C4C22⋊C411yescharacteristic
393(C2×D11)⋊C4C22⋊C411yescharacteristic
394(C2×D11)⋊C4C22⋊C411yescharacteristic
395C4⋊Dic11—21no—
396C4⋊Dic11—21no—
397Dic11⋊C4—21no—
398Dic11⋊C4—21no—
399Dic11⋊C4—21no—
400Dic11⋊C4—21no—
401Dic11⋊C4—42no—
402Dic11⋊C4—42no—
403Dic11⋊C4C22⋊C411yescharacteristic
404Dic11⋊C4C22⋊C411yescharacteristic
405Dic11⋊C4C22⋊C411yescharacteristic
406Dic11⋊C4C22⋊C411yescharacteristic
407C4×Dic11—21no—
408C4×Dic11—21no—
409C4×Dic11—21no—
410C4×Dic11—21no—
411C4×Dic11—21no—
412C4×Dic11—21no—
413C4×Dic11C22×C411yescharacteristic
414C4×Dic11C22×C411yescharacteristic
415C4×Dic11C2×D411yescharacteristic
416C4×Dic11C2×D411yescharacteristic
417#4318—21no—
418#4318—21no—
419#4318—21no—
420#4318—42no—
421#4318C2×D412yescomplemented
422C2×C11⋊C8—21no—
423C2×C11⋊C8—21no—
424C2×C11⋊C8—42no—
425#4313—42no—
426C8×D11—42no—
427D4×#41—111no—
428D4×M16—111no—
429C2×#421—111no—
430C22×#104—111no—
431#2290—111no—
432#1980—111no—
433#1963—111no—
434#1897—111no—
435#1896D1111yescharacteristic, complemented
436#1871—111no—
437#1871—111no—
438#1806—111no—
439#1789—111no—
440#1789—111no—
441#1759—111no—
442C23×C11—21no—
443C23×C11—21no—
444C23×C11—22no—
445C23×C11—21no—
446C23×C11—41no—
447C23×C11C2×C22⋊C411yescharacteristic
448C23×C11C2×C22⋊C411yescharacteristic
449C23×C11C22×D411yescharacteristic
450C22×D11—21no—
451C22×D11—21no—
452C22×D11—21no—
453C22×D11—21no—
454C22×D11—41no—
455C22×D11—41no—
456C22×D11—42no—
457C22×D11—42no—
458C22×D11—42no—
459C22×D11—42no—
460C22×D11—81no—
461C22×D11—81no—
462C22×D11C2×C22⋊C411yescharacteristic
463C22×D11C2×C22⋊C411yescharacteristic
464Q8×C11—21no—
465Q8×C11—21no—
466D4×C11—21no—
467D4×C11—21no—
468D4×C11—41no—
469D4×C11—41no—
470D4×C11—42no—
471D4×C11—81no—
472C2×C4×C11—21no—
473C2×C4×C11—21no—
474C2×C4×C11—21no—
475C2×C4×C11—21no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—21no—
479C2×C4×C11—21no—
480C2×C4×C11—21no—
481C2×C4×C11—21no—
482C2×C4×C11—22no—
483C2×C4×C11—21no—
484C2×C4×C11—21no—
485C2×C4×C11—21no—
486C2×C4×C11—22no—
487C2×C4×C11—41no—
488C2×C4×C11—41no—
489C2×C4×C11—41no—
490C2×C4×C11—48no—
491C2×C4×C11—41no—
492C2×C4×C11—41no—
493C2×C4×C11—41no—
494C2×C4×C11C2×C22⋊C411yescharacteristic
495C2×C4×C11C2×C22⋊C411yescharacteristic
496C2×C4×C11C23×C411yescharacteristic
497C2×C4×C11C22×D411yescharacteristic
498C2×C4×C11C22×D411yescharacteristic
499C2×C4×C11C2×#4111yescharacteristic
500C2×C4×C11H(5,𝔽2)11yescharacteristic
501C2×C4×C11H(5,𝔽2)11yescharacteristic
502C22⋊D11—22no—
503C22⋊D11—22no—
504C22⋊D11—22no—
505C22⋊D11—22no—
506C22⋊D11—41no—
507C22⋊D11—41no—
508C22⋊D11—42no—
509C22⋊D11—42no—
510C22⋊D11—42no—
511C22⋊D11—42no—
512C22⋊D11—42no—
513C22⋊D11—41no—
514C22⋊D11—41no—
515C22⋊D11—81no—
516C2×Dic11—21no—
517C2×Dic11—21no—
518C2×Dic11—21no—
519C2×Dic11—21no—
520C2×Dic11—41no—
521C2×Dic11—41no—
522C2×Dic11—42no—
523C2×Dic11—42no—
524C2×Dic11—41no—
525C2×Dic11—41no—
526C2×Dic11—41no—
527C2×Dic11—41no—
528C2×Dic11—41no—
529C2×Dic11—41no—
530C2×Dic11C2×C22⋊C411yescharacteristic
531C2×Dic11C2×C22⋊C411yescharacteristic
532C2×Dic11C2×C22⋊C411yescharacteristic
533C2×Dic11C2×C22⋊C411yescharacteristic
534C2×Dic11C2×C22⋊C411yescharacteristic
535C2×Dic11C2×C22⋊C411yescharacteristic
536D44—21no—
537D44—21no—
538D44—21no—
539D44—42no—
540D44—42no—
541D44—42no—
542D44—81no—
543D44C4×D412yes—
544C4×D11—21no—
545C4×D11—21no—
546C4×D11—21no—
547C4×D11—21no—
548C4×D11—21no—
549C4×D11—21no—
550C4×D11—22no—
551C4×D11—21no—
552C4×D11—21no—
553C4×D11—22no—
554C4×D11—42no—
555C4×D11—42no—
556C4×D11—42no—
557C4×D11—42no—
558C4×D11—42no—
559C4×D11—41no—
560C4×D11—41no—
561C4×D11—81no—
562Dic22—21no—
563Dic22—21no—
564Dic22—21no—
565Dic22—42no—
566Dic22—42no—
567Dic22C4×D412yes—
568C8×C11—41no—
569C8×C11—41no—
570C11⋊C8—22no—
571C11⋊C8—41no—
572C22×#41—111no—
573C22×#41—111no—
574C22×M16—111no—
575C22×M16—111no—
576#550—111no—
577D4×Q8—111no—
578#548—111no—
579#548—111no—
580#547—111no—
581#547—221no—
582#546—111no—
583#546—111no—
584#546—221no—
585#546—221no—
586D42—111no—
587D42—221no—
588#532—111no—
589#532—221no—
590#525—111no—
591#525—221no—
592#525—221no—
593#525C2×D1111yescharacteristic
594C4×#41—111no—
595C2×C4×D4—111no—
596C2×C4×D4—221no—
597C2×#117—111no—
598C22×C42C2×D1111yescharacteristic, complemented
599#436—221no—
600#435—221no—
601#435—221no—
602C8×D4—221no—
603#423—111no—
604#421—224no—
605C2×#104—111no—
606C2×#104—111no—
607C2×#104—111no—
608C2×#104—111no—
609C2×#104—111no—
610C2×#104—111no—
611C2×#104—111no—
612C2×#104—111no—
613C2×#104—111no—
614C2×#104—111no—
615C2×#104—224no—
616C2×#104C2×D1111yescharacteristic, complemented
617C2×#104C2×D1111yescharacteristic, complemented
618#407—111no—
619#407C2×D1111yescharacteristic, complemented
620C4×M16—111no—
621#388—221no—
622#387—221no—
623#386—221no—
624#385—221no—
625C4×C4⋊C4—111no—
626C4×C22⋊C4—111no—
627C4×C22⋊C4—111no—
628#376—111no—
629#339—111no—
630#339—111no—
631#339C2×D1111yescharacteristic, complemented
632#339C2×D1111yescharacteristic, complemented
633C22×C11—21no—
634C22×C11—21no—
635C22×C11—21no—
636C22×C11—21no—
637C22×C11—21no—
638C22×C11—21no—
639C22×C11—21no—
640C22×C11—42no—
641C22×C11—42no—
642C22×C11—41no—
643C22×C11—41no—
644C22×C11—41no—
645C22×C11#42112yescomplemented
646C22×C11C22×C22⋊C411yescharacteristic
647C22×C11D4211yescharacteristic
648C22×C11#54611yescharacteristic
649C2×D11—21no—
650C2×D11—21no—
651C2×D11—22no—
652C2×D11—21no—
653C2×D11—21no—
654C2×D11—21no—
655C2×D11—21no—
656C2×D11—41no—
657C2×D11—41no—
658C2×D11—41no—
659C2×D11—41no—
660C2×D11—41no—
661C2×D11—81no—
662C2×D11—81no—
663C2×D11—84no—
664C2×D11—84no—
665C4×C11—21no—
666C4×C11—21no—
667C4×C11—42no—
668C4×C11—42no—
669C4×C11—41no—
670C4×C11—41no—
671C4×C11—41no—
672C4×C11C2×C4×D411yescharacteristic
673C4×C11#51811yescharacteristic
674C4×C11D4211yescharacteristic
675C4×C11#54611yescharacteristic
676Dic11—22no—
677Dic11—21no—
678Dic11—21no—
679Dic11—21no—
680Dic11—21no—
681Dic11—21no—
682Dic11—21no—
683Dic11—41no—
684Dic11—81no—
685Dic11—81no—
686C2×#41—111no—
687C2×#41—111no—
688C2×#41—111no—
689C2×#41—111no—
690C2×#41—111no—
691C2×#41—111no—
692C2×#41—221no—
693C2×#41—222no—
694C2×#41—222no—
695C2×#41—221no—
696C2×#41—221no—
697C2×#41—221no—
698C2×#41—222no—
699C2×#41—222no—
700C2×#41—441no—
701C2×#41—441no—
702C2×#41—441no—
703C2×#41—441no—
704C2×#41C22×D1111yescharacteristic
705C22×Q8—111no—
706C22×Q8—111no—
707C22×D4—111no—
708C22×D4—111no—
709C22×D4—111no—
710C22×D4—221no—
711C22×D4—221no—
712C22×D4—221no—
713C23×C4—21no—
714C23×C4—111no—
715C23×C4—221no—
716C23×C4—221no—
717C23×C4C22×D1111yescharacteristic
718C2×M16—111no—
719C2×M16—111no—
720C2×M16—221no—
721C2×M16—221no—
722C2×M16—222no—
723C2×M16—222no—
724C2×M16—441no—
725C2×M16—441no—
726C2×M16C22×D1111yescharacteristic
727C2×M16C22×D1111yescharacteristic
728C22×C8—221no—
729C22×C8—221no—
730C4⋊Q8—111no—
731C4⋊Q8—221no—
732#127—111no—
733#127—221no—
734#124—111no—
735#124—111no—
736#124—221no—
737#124—221no—
738#123—21no—
739#123—221no—
740#123—221no—
741#123—221no—
742#123—221no—
743#123—221no—
744C22⋊Q8—111no—
745C22⋊Q8—111no—
746C22⋊Q8—221no—
747C22⋊Q8—221no—
748C22⋊Q8—221no—
749C22⋊Q8—221no—
750C22⋊Q8C4×D1111yescharacteristic
751C22⋊Q8C4×D1111yescharacteristic
752#121—111no—
753#121—111no—
754#121—221no—
755#121—221no—
756#121—221no—
757#121—221no—
758#121—221no—
759#121—221no—
760#121—221no—
761#121—221no—
762#121—221no—
763#121—221no—
764#121C4×D1111yescharacteristic
765#121C4×D1111yescharacteristic
766#120—21no—
767#120—221no—
768#120—221no—
769#120—221no—
770#120—221no—
771#120—221no—
772C4×Q8—111no—
773C4×Q8—111no—
774C4×D4—21no—
775C4×D4—21no—
776C4×D4—111no—
777C4×D4—111no—
778C4×D4—111no—
779C4×D4—111no—
780C4×D4—111no—
781C4×D4—111no—
782C4×D4—111no—
783C4×D4—111no—
784C4×D4—111no—
785C4×D4—111no—
786C4×D4—221no—
787C4×D4—221no—
788C4×D4—221no—
789C4×D4—221no—
790C4×D4—221no—
791C4×D4—221no—
792C4×D4—221no—
793C4×D4—221no—
794C4×D4—221no—
795C4×D4—221no—
796#117—221no—
797#117—222no—
798#117—441no—
799#117C22×D1111yescharacteristic
800C2×C4⋊C4—111no—
801C2×C4⋊C4—221no—
802C2×C4⋊C4—221no—
803C2×C4⋊C4—221no—
804C2×C22⋊C4—111no—
805C2×C22⋊C4—111no—
806C2×C22⋊C4—221no—
807C2×C22⋊C4—221no—
808C2×C22⋊C4—221no—
809C2×C22⋊C4—221no—
810C2×C22⋊C4—221no—
811C2×C42—22no—
812C2×C42—21no—
813C2×C42—41no—
814C2×C42—111no—
815C2×C42—111no—
816C2×C42—111no—
817C2×C42—221no—
818C2×C42C22×D1111yescharacteristic
819C2×C42C22×D1111yescharacteristic
820C4⋊C8—221no—
821C4⋊C8—221no—
822#104—22no—
823#104—41no—
824#104—114no—
825#104—222no—
826#104—222no—
827#104—222no—
828#104—222no—
829#104—222no—
830#104—222no—
831#104—441no—
832#104—441no—
833#104—441no—
834C22⋊C8—21no—
835C22⋊C8—21no—
836C22⋊C8—221no—
837C22⋊C8—221no—
838#97—221no—
839C4×C8—221no—
840#95—221no—
841#95—221no—
842#95—221no—
843#95—221no—
844#95—221no—
845C2×C11—21no—
846C2×C11—21no—
847C2×C11—22no—
848C2×C11—41no—
849C2×C11—81no—
850C2×C11D4×C22⋊C411yescharacteristic
851C2×C11C2×#42111yescharacteristic
852C2×C11#290111yescharacteristic
853D11—41no—
854D11—41no—
855D11—42no—
856D11—81no—
857C24—111no—
858C24—221no—
859C24—221no—
860C24D4×D1111yescharacteristic
861#41—21no—
862#41—21no—
863#41—21no—
864#41—21no—
865#41—112no—
866#41—112no—
867#41—222no—
868#41—222no—
869#41—221no—
870#41—221no—
871#41—222no—
872#41—222no—
873#41—221no—
874#41—221no—
875#41—221no—
876#41—221no—
877#41—442no—
878#41—442no—
879#41—441no—
880#41—441no—
881#41—442no—
882#41—442no—
883#41—442no—
884#41—442no—
885#41—441no—
886#41—442no—
887#41—442no—
888#41—441no—
889C2×Q8—111no—
890C2×Q8—111no—
891C2×Q8—221no—
892C2×Q8—222no—
893C2×Q8—221no—
894C2×Q8—222no—
895C2×Q8—441no—
896C2×Q8—441no—
897C2×Q8C2×C4×D1111yescharacteristic
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—111no—
902C2×D4—111no—
903C2×D4—111no—
904C2×D4—111no—
905C2×D4—111no—
906C2×D4—111no—
907C2×D4—222no—
908C2×D4—221no—
909C2×D4—221no—
910C2×D4—221no—
911C2×D4—221no—
912C2×D4—221no—
913C2×D4—221no—
914C2×D4—222no—
915C2×D4—221no—
916C2×D4—221no—
917C2×D4—221no—
918C2×D4—221no—
919C2×D4—221no—
920C2×D4—221no—
921C2×D4—441no—
922C2×D4—441no—
923C2×D4—442no—
924C2×D4—442no—
925C2×D4—444no—
926C2×D4—442no—
927C2×D4—442no—
928C2×D4—442no—
929C2×D4C2×C4×D1111yescharacteristic
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—111no—
941C22×C4—111no—
942C22×C4—111no—
943C22×C4—111no—
944C22×C4—111no—
945C22×C4—111no—
946C22×C4—111no—
947C22×C4—221no—
948C22×C4—221no—
949C22×C4—221no—
950C22×C4—221no—
951C22×C4—221no—
952C22×C4—221no—
953C22×C4—221no—
954C22×C4—221no—
955C22×C4—221no—
956C22×C4—221no—
957C22×C4—221no—
958C22×C4—221no—
959C22×C4—221no—
960C22×C4—221no—
961C22×C4—221no—
962C22×C4—221no—
963C22×C4—442no—
964C22×C4—442no—
965C22×C4—442no—
966C22×C4—442no—
967C22×C4C2×C4×D1111yescharacteristic
968C22×C4C2×C4×D1111yescharacteristic
969C22×C4D4×D1111yescharacteristic
970C22×C4D4×D1111yescharacteristic
971C22×C4D4×D1111yescharacteristic
972C22×C4C23×D1111yescharacteristic
973M16—21no—
974M16—21no—
975M16—21no—
976M16—21no—
977M16—112no—
978M16—221no—
979M16—221no—
980M16—221no—
981M16—442no—
982M16—442no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—221no—
986C2×C8—221no—
987C2×C8—442no—
988C2×C8—442no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—111no—
992C4⋊C4—111no—
993C4⋊C4—111no—
994C4⋊C4—111no—
995C4⋊C4—221no—
996C4⋊C4—221no—
997C4⋊C4—221no—
998C4⋊C4—221no—
999C4⋊C4—221no—
1000C4⋊C4—221no—
1001C4⋊C4—442no—
1002C4⋊C4—442no—
1003C4⋊C4C2×C4×D1111yescharacteristic
1004C4⋊C4C2×C4×D1111yescharacteristic
1005C22⋊C4—21no—
1006C22⋊C4—21no—
1007C22⋊C4—21no—
1008C22⋊C4—21no—
1009C22⋊C4—21no—
1010C22⋊C4—111no—
1011C22⋊C4—111no—
1012C22⋊C4—111no—
1013C22⋊C4—111no—
1014C22⋊C4—111no—
1015C22⋊C4—111no—
1016C22⋊C4—111no—
1017C22⋊C4—111no—
1018C22⋊C4—221no—
1019C22⋊C4—221no—
1020C22⋊C4—221no—
1021C22⋊C4—221no—
1022C22⋊C4—221no—
1023C22⋊C4—221no—
1024C22⋊C4—221no—
1025C22⋊C4—221no—
1026C22⋊C4—221no—
1027C22⋊C4—221no—
1028C22⋊C4—442no—
1029C22⋊C4—442no—
1030C22⋊C4—442no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—42no—
1036C42—111no—
1037C42—111no—
1038C42—111no—
1039C42—111no—
1040C42—221no—
1041C42—221no—
1042C42—221no—
1043C42—221no—
1044C42—221no—
1045C42—221no—
1046C42D4×D1112yescomplemented
1047C11#2243411yescharacteristic, complemented, Sylow
1048C23—21no—
1049C23—21no—
1050C23—22no—
1051C23—21no—
1052C23—41no—
1053C23—111no—
1054C23—111no—
1055C23—221no—
1056C23—221no—
1057C23—221no—
1058C23—221no—
1059C23—441no—
1060C23—441no—
1061C23—442no—
1062C23—442no—
1063C23—442no—
1064C23—442no—
1065C23—881no—
1066C23—881no—
1067C23C22⋊C4×D1111yescharacteristic
1068C23C22⋊C4×D1111yescharacteristic
1069C23C2×D4×D1111yescharacteristic
1070Q8—21no—
1071Q8—21no—
1072Q8—112no—
1073Q8—221no—
1074Q8—221no—
1075Q8—221no—
1076Q8—442no—
1077Q8—442no—
1078D4—21no—
1079D4—21no—
1080D4—41no—
1081D4—41no—
1082D4—42no—
1083D4—81no—
1084D4—112no—
1085D4—222no—
1086D4—222no—
1087D4—222no—
1088D4—222no—
1089D4—221no—
1090D4—221no—
1091D4—221no—
1092D4—442no—
1093D4—442no—
1094D4—442no—
1095D4—441no—
1096D4—441no—
1097D4—442no—
1098D4—442no—
1099D4—442no—
1100D4—442no—
1101D4—442no—
1102D4—441no—
1103D4—441no—
1104D4—881no—
1105D4—881no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—22no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—22no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—48no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—111no—
1129C2×C4—111no—
1130C2×C4—111no—
1131C2×C4—111no—
1132C2×C4—111no—
1133C2×C4—111no—
1134C2×C4—221no—
1135C2×C4—221no—
1136C2×C4—221no—
1137C2×C4—221no—
1138C2×C4—221no—
1139C2×C4—221no—
1140C2×C4—221no—
1141C2×C4—221no—
1142C2×C4—221no—
1143C2×C4—222no—
1144C2×C4—221no—
1145C2×C4—221no—
1146C2×C4—222no—
1147C2×C4—221no—
1148C2×C4—442no—
1149C2×C4—442no—
1150C2×C4—442no—
1151C2×C4—442no—
1152C2×C4—442no—
1153C2×C4—441no—
1154C2×C4—441no—
1155C2×C4—442no—
1156C2×C4—442no—
1157C2×C4—441no—
1158C2×C4—441no—
1159C2×C4—441no—
1160C2×C4—441no—
1161C2×C4—441no—
1162C2×C4—441no—
1163C2×C4—441no—
1164C2×C4—441no—
1165C2×C4—881no—
1166C2×C4C22⋊C4×D1111yescharacteristic
1167C2×C4C22⋊C4×D1111yescharacteristic
1168C2×C4C22×C4×D1111yescharacteristic
1169C2×C4C2×D4×D1111yescharacteristic
1170C2×C4C2×D4×D1111yescharacteristic
1171C2×C4#6703711yescharacteristic
1172C2×C4#41×D1111yescharacteristic
1173C2×C4#6704211yescharacteristic
1174C8—41no—
1175C8—41no—
1176C8—222no—
1177C8—441no—
1178C22—21no—
1179C22—21no—
1180C22—21no—
1181C22—21no—
1182C22—21no—
1183C22—21no—
1184C22—21no—
1185C22—42no—
1186C22—42no—
1187C22—41no—
1188C22—41no—
1189C22—41no—
1190C22—221no—
1191C22—221no—
1192C22—222no—
1193C22—221no—
1194C22—221no—
1195C22—221no—
1196C22—221no—
1197C22—441no—
1198C22—441no—
1199C22—441no—
1200C22—441no—
1201C22—441no—
1202C22—881no—
1203C22—881no—
1204C22—884no—
1205C22—884no—
1206C22#1062243412yescomplemented
1207C22C2×C22⋊C4×D1111yescharacteristic
1208C22#1062312111yescharacteristic
1209C22#1062318511yescharacteristic
1210C4—21no—
1211C4—21no—
1212C4—42no—
1213C4—42no—
1214C4—41no—
1215C4—41no—
1216C4—41no—
1217C4—221no—
1218C4—221no—
1219C4—222no—
1220C4—221no—
1221C4—221no—
1222C4—221no—
1223C4—221no—
1224C4—441no—
1225C4—881no—
1226C4—881no—
1227C4C4×D4×D1111yescharacteristic
1228C4#1062307611yescharacteristic
1229C4#1062314011yescharacteristic
1230C4#1062314111yescharacteristic
1231C2—21no—
1232C2—21no—
1233C2—22no—
1234C2—41no—
1235C2—81no—
1236C2—441no—
1237C2—441no—
1238C2—442no—
1239C2—881no—
1240C2#1307143411yescharacteristic
1241C2C2×#1062243411yescharacteristic
1242C2#1307716011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1896C2
socleC22×C11C22×C22⋊C4
prime radical#13082099C2
cosocleC22×C4×C11C24
hypercenter#1896D11
hypocenterC11#22434
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1896

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #13077348C2semidirect
3. C2×#10622434C2semidirect
4. C22×#66869C2semidirect
5. #13071059C2semidirect
6. #13069533C2semidirect
7. #13069446C2semidirect
8. #13069063C2semidirect
9. #13068919C2semidirect
10. #13068917C2semidirect
11. #13068635C2semidirect
12. #13068559C2semidirect
13. #13068558C2semidirect
14. #13068425C2semidirect
15. C11×#1896C2semidirect
19. C22×C42×C11C22semidirect
22. C22×#4318C22semidirect
23. C2×M16×D11C22semidirect
26. #10623164C4semidirect
27. #10623163C4semidirect
28. #10623162C4semidirect
29. #10623161C4semidirect
30. #10623143C4semidirect
31. #10623140C4semidirect
32. #10623130C4semidirect
33. #10623129C4semidirect
42. C2×#66925C22semidirect
43. C2×C11×#104C22semidirect
44. C2×C11×#104C22semidirect
45. C11×#407C22semidirect
46. C2×#66901C22semidirect
47. C2×#66901C22semidirect
50. C4×C22⋊Dic11C22semidirect
53. C2×#66889C22semidirect
54. C2×#66889C22semidirect
55. #10622739C22semidirect
56. #10622731C22semidirect
57. M16×Dic11C22semidirect
59. C4×(C2×D11)⋊C4C22semidirect
61. #10622545C22semidirect
62. C4×Dic11⋊C4C22semidirect
66. C2×#66869C22semidirect
67. C2×#66869C22semidirect
73. C11×#339C22semidirect
74. C11×#339C22semidirect
75. #10622170C22semidirect
76. #10622170C22semidirect
86. C2×#4343C2×C4semidirect
87. C2×Q8×D11C2×C4semidirect
89. C2×#4341C2×C4semidirect
92. C2×D4×D11C2×C4semidirect
127. #67000C2×C4semidirect
128. #66997C2×C4semidirect
130. #66993C2×C4semidirect
138. #66989C2×C4semidirect
169. #66950C2×C4semidirect
170. #66950C2×C4semidirect
174. #66948C2×C4semidirect
175. #66948C2×C4semidirect
179. #66946C2×C4semidirect
180. #66946C2×C4semidirect
183. #66940C2×C4semidirect
184. #66940C2×C4semidirect
235. #66869D4semidirect
373. C42×C11C2×D4semidirect
421. #4318C2×D4semidirect
435. #1896D11semidirect
598. C22×C42C2×D11semidirect
616. C2×#104C2×D11semidirect
617. C2×#104C2×D11semidirect
619. #407C2×D11semidirect
631. #339C2×D11semidirect
632. #339C2×D11semidirect
645. C22×C11#421semidirect
1046. C42D4×D11semidirect
1047. C11#22434semidirect
1206. C22#10622434semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130820992
#130773482
C2×#106224342
C22×#668692
#130710592
#130695332
#130694462
#130690632
#130689192
#130689172
#130686352
#130685592
#130685582
#130684252
C11×#18962
#2243411